I agree with you on your first paragraph however the real problems between the 2 sides started in 1948 with a climax in 1967 (ignoring 1973).
And yes Israel hasn't called for annihilation of any country or region but they use a more subtle way, they keep on expanding their settlements and the ultimate result is the same.
About conquering; didn't Florida, Texas, New Mexico, Arizona, California once belong to Mexico ?